Question: Simplify to lowest terms. $\dfrac{40}{24}$
Explanation: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 40 and 24? $40 = 2\cdot2\cdot2\cdot5$ $24 = 2\cdot2\cdot2\cdot3$ $\mbox{GCD}(40, 24) = 2\cdot2\cdot2 = 8$ $\dfrac{40}{24} = \dfrac{5 \cdot 8}{ 3\cdot 8}$ $\hphantom{\dfrac{40}{24}} = \dfrac{5}{3} \cdot \dfrac{8}{8}$ $\hphantom{\dfrac{40}{24}} = \dfrac{5}{3} \cdot 1$ $\hphantom{\dfrac{40}{24}} = \dfrac{5}{3}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{40}{24}= \dfrac{2\cdot20}{2\cdot12}= \dfrac{2\cdot 2\cdot10}{2\cdot 2\cdot6}= \dfrac{2\cdot 2\cdot 2\cdot5}{2\cdot 2\cdot 2\cdot3}= \dfrac{5}{3}$